A recent City Hall press release pulled the curtain back on a jaw-dropping statistic: Gotham’s social-services agency offers “vital services to more than 3 million New Yorkers.”

Feel free to read that again: Three million New Yorkers get basic services from the city. Out of 8 million residents.

That’s 38 percent of the population.

That’s stunning.

How could things have come to this pass? Surely, there can’t be that many folks unable to care for themselves.

Still, it’s human nature to tend to covet free things – and for pols to pander to base instincts.

The press release – which announced the appointment of Robert Doar as the new head for the city’s Human Resources Administration and Department of Social Services – laid out the vast range of services offered:

Still, many local pols (e.g., most everyone at the City Council) think New York doesn’t provide enough services. They won’t be happy until 100 percent of city dwellers are on one form of welfare or another.

Certainly, those who can’t provide for themselves warrant assistance.

But 38 percent of the city?

That can’t possibly be correct.

Even if it is, the costs are unsustainable.

True, the strong local economy (with special thanks to Wall Street) has fueled a surge in tax revenues, masking any long-term budget woes.

But Wall Street is famous for its ups and downs. And when the local economy slows, so do tax revenues – even as the demand for help at those times grows.

What will City Hall do for cash?

Hike tax rates again?

Sending those saddled with the hikes scurrying for refuge outside the city – and leaving an even larger proportion of residents in need of aid?

Last week’s press release did New Yorkers a huge favor by shining a spotlight – even if inadvertently – on a huge structural problem.

We wish Doar, the new welfare boss, the best of luck.

But here’s some free advice: Focus on trimming the welfare rolls.

Not expanding them.

A stockmarket downturn is all that stands between Gotham and a busted budget.

And those who suffer may be well more than the 38 percent who get aid.